An adjustable holding device for motor vehicle headlamps is discussed, for example, in German patent document DE-A-29 16 225. A motor vehicle headlamp is held there in a frame which is mounted, inter alia, by a ball and socket joint, on a base plate. The ball and socket joint comprises a threaded stud with a ball socket on the end side, in which a ball connected to the frame is accommodated. The ball is pressed here into the ball socket by elastic deformation thereof. The threaded stud is screwed into the main body such that the frame supporting the headlamp is pivotable about the ball and socket joint. In order to set a certain pivoted position of the frame supporting the headlamp in relation to a vertical and a horizontal pivot axis intersecting the ball and socket joint, two adjusting screws are provided. The frame is therefore held in relation to the main body via the ball and socket joint and the two adjusting screws and therefore by three receptacles. The set position of the headlamps is merely secured here by the friction of the adjusting screws in the associated internal threads on the main body. Furthermore, the deformation of the elastic joint socket causes a certain flexibility of the ball and socket joint, which is detrimental to precise setting or long-term maintaining of the sensor position.